# Decomposing Solution Sets of Polynomial Systems Using Derivatives

```@inproceedings{Brake2016DecomposingSS,
title={Decomposing Solution Sets of Polynomial Systems Using Derivatives},
author={Daniel A. Brake and Jonathan D. Hauenstein and Alan C. Liddell},
booktitle={International Congress on Mathematical Software},
year={2016}
}```
• Published in
International Congress on…
11 July 2016
• Mathematics, Computer Science
A core computation in numerical algebraic geometry is the decomposition of the solution set of a system of polynomial equations into irreducible components, called the numerical irreducible decomposition. One approach to validate a decomposition is what has come to be known as the “trace test.” This test, described by Sommese, Verschelde, and Wampler in 2002, relies upon path tracking and hence could be called the “tracking trace test.” We present a new approach which replaces path tracking…
6 Citations

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• 2015
In the field of numerical algebraic geometry, positive-dimensional solution sets of systems of polynomial equations are described by witness sets. In this paper, we define multiprojective witness

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The new approach extends previous work on success ratios of parameter homotopies to using monodromy loops as well as the addition of a trace test that provides a stopping criterion for validating that all solutions have been found.

### Identifiability and numerical algebraic geometry

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• 2019
Numerical algebraic geometry is used to determine if a model given by polynomial or rational ordinary differential equations is identifiable or unidentifiable, and a novel approach to compute the identifiability degree is presented.

### Multiprojective witness sets and a trace test

• Mathematics
• 2020
Abstract In the field of numerical algebraic geometry, positive-dimensional solution sets of systems of polynomial equations are described by witness sets. In this paper, we define multiprojective

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